Abstract: Piping is one of the common situations dangerous to embankment. Piping progression can be well simulated by using an approach that couples the two domains of seepage and pipe flow. The element-free method can add or delete a node easily, showing a great advantage in calculation of the dynamically moving boundary between the two domains. Compared with the element-free Galerkin method (EFG), a natural element method adopts shape functions that satisfy the Kronecker ? conditions, and hence it can achieve a better accuracy in the calculation of boundary conditions. On the basis of our previous work, we have applied this new method, as a substitute for the EFG method, to the simulation of piping progression. An example shows that this substitution is appropriate.